Abstract

We show that, for r = 1, 2, a graph G with 2n + 2 (6) vertices and maximum degree 2n + 1 - r is of Class 2 if and only if |E(G/v)| > () - rn, where v is a vertex of G of minimum degree, and we make a conjecture for 1 r n, of which this result is a special case. For r = 1 this result is due to Plantholt.